Find the value of K so that:

X^2+Kxy+ 2y^2+3x+5y+2=O

May represent a line pair.

Dear student

 

For a pair of straight line

 

Equate abc +2fgh - af² - bg² - ch² = 0

 

Hopw you understand.

 

Thanks and

the condition for a general quad eqn of the form ax^2+by^2+2gx+2fy+2hxy+c=0 to represent a pair of st lines (POSL) is that the determinant should be 0.

here a=1, b= 2, g= 3/2, f= 5/2, h= k/2, c=2, so we form the determinant as follows:

| 1     k/2  3/2|

| k/2  2     5/2|  =  0

|3/2   5/2    2 |

putting this det 0, we get K= 3, 9/2